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Duality property for positive weak Dunford-Pettis operators. (English) Zbl 1262.47057
The authors prove that an operator is weak Dunford-Pettis if its adjoint is, but the converse is in general false, and they produce some necessary and sufficient conditions under which each positive weak Dunford-Pettis operator has an adjoint which is weak Dunford-Pettis.
For basic terminologies and notations, the authors use [C. D. Aliprantis, Positive operators. Reprint of the 1985 original. Berlin: Springer (2006; Zbl 1098.47001)].

MSC:
47B65 Positive linear operators and order-bounded operators
46B42 Banach lattices
47B07 Linear operators defined by compactness properties
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[10] Z. L. Chen and A. W. Wickstead, “L-weakly and M-weakly compact operators,” Indagationes Mathematicae, vol. 10, no. 3, pp. 321-336, 1999. · Zbl 1028.47028 · doi:10.1016/S0019-3577(99)80025-1
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